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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 913 · 40 questions
TalentJR

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  2. 2.How many prime numbers are there between 60 and 80? (a) 6 (b) 5 (c) 4 (d) 7
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
  4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/11 (c) 1/12 (d) 2/11
  5. 5.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 15 (b) 55 (c) 60 (d) 110
  6. 6.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  8. 8.What are the roots of x² − 13x + 36 = 0? (a) 2 and 18 (b) 4 and 9 (c) 1 and 36 (d) 1 and 12
  9. 9.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
  10. 10.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 80° (d) 50°
  11. 11.In a class of 34 children, 23 like dance, 7 like music and 4 like both. How many like only dance? (a) 23 (b) 27 (c) 19 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  13. 13.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 15° (c) 110° (d) 85°
  14. 14.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 5 (d) 4
  15. 15.Which term of the AP 3, 11, 19, 27, … is 187? (a) 23rd (b) 25th (c) 26th (d) 24th
  16. 16.If a + b = 8 and ab = 12, what is (a − b)²? (a) 64 (b) 40 (c) 16 (d) 4
  17. 17.If a + b = 18 and ab = 80, what is (a − b)²? (a) 164 (b) 4 (c) 2 (d) 324
  18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
  19. 19.The mean of 7 numbers is 16. When the number 32 is added to them, what is the new mean? (a) 19 (b) 24 (c) 16 (d) 18
  20. 20.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2704 (b) 2714 (c) 2504 (d) 2304
  21. 21.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 12 (c) 70 (d) 35
  22. 22.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
  23. 23.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 120° (c) 300° (d) 60°
  24. 24.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
  25. 25.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 14 (b) 19 (c) 16 (d) 15
  26. 26.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
  27. 27.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 40 (b) 278 (c) 550 (d) 275
  28. 28.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
  29. 29.A bag has 3 blue, 7 red and 9 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 13/19 (b) 1/3 (c) 12/19 (d) 7/19
  30. 30.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
  31. 31.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
  32. 32.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1444 (b) 1764 (c) 1454 (d) 1596
  33. 33.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
  34. 34.What is the mean of 16, 4, 7 and 17? (a) 13 (b) 12 (c) 10 (d) 11
  35. 35.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 4366 (b) 5476 (c) 4884 (d) 4356
  36. 36.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 25 (d) 37
  37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
  38. 38.What is the mode of 13, 13, 4, 4, 12, 18 and 4? (a) 4 (b) 12 (c) 18 (d) 13
  39. 39.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 98 (c) 106 (d) 97
  40. 40.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 49 (c) 84 (d) 42

Answer key

  1. 289
  2. 5
  3. 16
  4. 1/18
  5. 55
  6. 16 times
  7. 3
  8. 4 and 9
  9. 1386 sq cm
  10. 50°
  11. 19
  12. 4
  13. 15°
  14. 5
  15. 24th
  16. 16
  17. 4
  18. 132 cm
  19. 18
  20. 2704
  21. 35
  22. 125 cu cm
  23. 60°
  24. (x + 8)(x + 9)
  25. 15
  26. 55°
  27. 275
  28. 10°
  29. 12/19
  30. 66
  31. 3/8
  32. 1444
  33. 2464 sq cm
  34. 11
  35. 4356
  36. 25
  37. 1/36
  38. 4
  39. 97
  40. 42

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